Moiré two-dimensional materials, formed by stacking 2D crystals with a lattice mismatch, exhibit significant transformations in their electronic and phononic properties due to interference patterns in their atomic arrangements. These transformations give rise to various emergent phenomena absent in the original materials, such as superconductivity and even a fractional quantum Hall effect in the absence of a magnetic field. In this talk, I will provide an overview of the current research landscape in moiré-stacked 2D materials, including recent experimental and theoretical advances. I will introduce the basic continuum theories that describe moiré electronic systems and highlight recent developments in a variety of moiré 2D materials, quasiperiodic systems, and moiré phonons, which exhibit properties distinct from those of conventional atomic crystals.